Check the facts before you switch

A made-up example built from a parent's description. A way, never the way.

Guide: Omar · Learner: Beth · Age band: 7–9 · Subject: Math

Where the learner was stuck

Beth, who is nine, worked through one maths programme to the end of its grade-four material, and there multi-digit multiplication and long division came apart. She sets a two-digit-by-one-digit problem out neatly and then stalls, or carries the wrong number, or loses her place partway down a long division. Omar's read was that the programme had stopped working and it was time to switch to another one — the question he brought was which. But the trouble was not really the programme. Watching Beth, the carrying and the dividing fell apart in the same place every time: at the moment she needed a times-table fact and did not have it to hand, so she stopped to count it out, lost the thread of the bigger procedure, and the whole thing collapsed. The stuck point was underneath the multiplication, not in it — and a new programme would land her at the very same spot.

The approach (built through what they love)

Before changing anything, Omar does a five-minute check to find the one topic that is actually wobbling — the same idea a companion sample, find-the-earliest-gap-stepping-stones.md, lays out for mixed early gaps, pointed here at one maths procedure. It has three quick steps. First, the facts: he runs through the times tables and sorts each one, with Beth, into the ones she just knows and the ones she counts out — not to score her, just to see. Second, place value, and here Beth's own thing does the work: she loves the coin jar, and she already trades ten pennies for a dime without thinking. That trade is place value — ten ones regrouped as one ten — and the same trade is exactly what carrying and long division lean on. He lays out one number in coins and has her say it as tens and ones. Third, a single two-digit-by-one-digit problem, talked through out loud, so he can hear where it breaks. Almost always it breaks at a fact that is not automatic. So the fix is not a new programme: it is five minutes a day on the handful of facts that are still counted out — the strategy-first way the companion sample math-facts-fluency-dominoes.md describes — and only once those facts come without counting does Omar judge whether the programme itself is the problem.

For the guide: the shape of a session

The check is short and kind — five minutes, not an exam. Say what it is first: "We are finding the one thing to fix, not testing you." Run the facts and simply note which are instant and which get counted; two seconds and moving lips is a counted one. Do the coin step next: can Beth say a number as tens and ones, and trade ten ones for a ten without having to think? Then one multiplication problem, out loud, and listen for the exact moment it breaks. You are looking for the earliest wobble, not the latest — the counted fact underneath the failed carry, not the failed carry itself. Then the daily work is five minutes on those facts, most days, stopping while it is going well. Keep a short note of which facts are still counted so each session starts where the last left off. Do not switch programmes yet; give the facts a few weeks first, and judge the programme only against a child who now has them.

What only a person can do

Omar can hear the difference between Beth recalling six times seven and Beth quietly counting it under her breath — the same answer arrives, but only one of them is the skill the multiplication needs. He can tell a carry that failed because the procedure is shaky from a carry that failed because the fact underneath was missing, and chase the earlier one. He can watch one talked-through problem and locate, in a few seconds, the single place it breaks — something no finished worksheet, marked right or wrong at the end, can show him. And he can decide, before spending months on a different programme, whether the programme was ever the problem at all. A page can mark the answer; only a person can find the reason.

Where the learner leads

Beth leads the coins. She sorts the jar better than Omar does and already knows, without being told, that ten pennies make a dime and ten dimes make a dollar's worth — trading up a handful of small coins for one bigger one as a matter of course. That trade is the whole of place value, and it is already hers. Omar's part is to name it: the swap she does in the coin jar — ten ones become one ten, and you write the one in the next column along — is the very move that carries in multiplication and regroups in long division. She supplies the trading; he points out that the thing she finds obvious with coins is the thing the hard problems are built on.

The game on the learner's side

The game is a hand-played sorting game with the facts and the coin jar, no screen involved. It comes in two small piles and three levels. First Beth meets a times-table fact on a card and drops it into one of two piles — "I just know it" or "I had to work it out" — which turns the five-minute check into something she runs herself and can watch shrink as the worked-out pile gets smaller week by week. Level one is the facts she counts most, a few at a time; level two takes a fact from the "know it" pile and builds its answer in coins, trading ten ones for a ten out loud; level three talks a whole two-digit-by-one-digit problem through with the coins on the table, carrying by trading. It steps up as the "work it out" pile shrinks and eases back when a new set of facts goes in. Nothing is marked wrong — a counted fact just goes back in the pile for tomorrow's five minutes. It is played by hand with cards and coins; it is not a game to switch on.

When to seek an evaluation

Needing to count out some facts at nine, and having multi-digit work wobble because of it, is ordinary, and for most children a few weeks of short daily fact practice is enough for the bigger procedures to steady. But if, after a long stretch of patient five-minute sessions, the facts still will not stick and every one is rebuilt from counting, or if numbers and amounts seem to slip and rearrange in ways the child cannot catch or correct, or if the same sharp effort shows up across many kinds of work and not only in maths, it can be worth describing what you see to someone whose work is understanding how children learn. A family doctor or an early-learning specialist can watch, ask questions, and tell you what they see. You do not need a label to have that conversation, and what you learn is yours to use however you choose.

A way, never the way

A five-minute check before switching is one way to tell the programme from the one topic underneath it, chosen here because the trouble sat under the multiplication rather than in it. Another family would get at the same thing with a number line, finger patterns, or base-ten blocks instead of a coin jar. The parts worth keeping are the order: check the facts first, then place value, then one problem talked through; find the earliest wobble, not the latest; fix it with five minutes a day and stop on a win; and judge the programme only after, not before. The companion samples find-the-earliest-gap-stepping-stones.md and math-facts-fluency-dominoes.md carry the same two moves — find the first gap, make the facts automatic — further. The goal is to fix the right thing before changing everything. What you check with, and whether you switch in the end, is yours to choose.